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Invariant tori for asymptotically linear impact oscillators

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Science china mathematics 2006年第5期49卷 669-687页

作者： QIAN Dingbian & SUN Xiying School of Mathematical sciences, Suzhou university, Suzhou 215006, china laboratory of mathematics for nonlinear sciences, fudan university, shanghai 200433, china School of Mathematical sciences Suzhou University Suzhou China laboratory of mathematics for nonlinear sciences Fudan University Shanghai China

The existence of invariant tori and quasi-periodic solutions for asymptotically linear impact oscillators is proved by using the successor map and some generalized versions of the Moser's twist theorem.

关键词： invariant tori, boundedness of solutions, quasi-periodic solution, impact oscillator.

A New Approach to Synchronization Analysis of Linearly Coupled Map Lattices

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Chinese Annals of mathematics,Series B 2007年第2期28卷 149-160页

作者： Wenlian LU Tianping CHENt Published online March School of Mathematical sciences and laboratory of mathematics for nonlinear sciences Fudan University Shanghai 200433 China.

In this paper, a new approach to analyze synchronization of linearly coupled map lattices （LCMLs） is presented. A reference vector x（t） is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection. By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and right eigenvectors corresponding to the eigenvalue ＂0＂ of the coupling matrix play key roles in the stability of synchronization manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not converge to a certain knowable s（t） satisfying s（tT1） = f（s（t）） but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each x^i（t） for i=1,……, m, but not a solution s（t） satisfying s（t ＋ 1）=f（s（t））.

关键词： Linearly coupled map lattices Synchronization Synchronizationmanifold Local stability of synchronization manifold Global stability of synchronization manifold

Fredholm operators in Toeplitz algebras associated with discrete abelian groups

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Chinese Science Bulletin 1998年第14期43卷 1175-1179页

作者： XU Qingxiang 1 and CHEN Xiaoman 2 1. Department of mathematics, shanghai Normal university, shanghai 200234, china 2. laboratory of mathematics for nonlinear sciences and Institute of mathematics, fudan university, shanghai 200433, china Department of mathematics Shanghai Normal University Shanghai China laboratory of mathematics for nonlinear sciences and Institute of mathematics Fudan University Shanghai China

The locally finite below sets are introduced and the Fredholm operators in Toeplitz algebras associated with discrete abelian groups are studied.

关键词： discrete abelian group quasi_ordered group Toeplitz operator Fredholm operator.

SOME REMARKS ON THE NULL CONDITION FOR nonlinear ELASTODYNAMIC SYSTEM

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Chinese Annals of mathematics,Series B 2002年第3期23卷 311-316页

作者： XIN JIE Institute of mathematics, laboratory of mathematics for nonlinear sciences, Pudan university, shanghai 200433, china. Institute of mathematics Laboratory of Mathematics for Nonlinear Sciences Fudan University Shanghai 200433 China

The author derives the same null condition as in [1] for the nonlinear elastodynamic system in a simpler way and proves the equivalence of the null conditions introduced in [1] and [7] respectively.

关键词： Null condition Stored energy function Elastodynamic system

Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

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Chinese Annals of mathematics,Series B 2011年第5期32卷 771-780页

作者： Yi ZHOU 11 Key laboratory of mathematics for nonlinear sciences,Ministry of Education,china shanghai Key laboratory for Contemporary Applied mathematics School of Mathematical sciences,fudan university,shanghai 200433,china. Key laboratory of mathematics for nonlinear sciences Ministry of Education China shanghai Key laboratory for Contemporary Applied mathematics School of Mathematical sciences Fudan University Shanghai China

The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic *** the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in *** ***.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.

关键词： Cauchy problem Global classical solution Partially dissipativequasilinear hyperbolic system

Sharpness on the Lower Bound of the Lifespan of Solutions to nonlinear Wave Equations

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Chinese Annals of mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 nonlinear Mathematical Modeling and Methods laboratory shanghai Key laboratory for Contem- porary Applied mathematics School of Mathematical sciences, fudan university, shanghai 200433, china. 2 School of Mathematical sciences, fudan university, shanghai 200433, china Department of mathematics, North university of china, Taiyuan 030051, china. nonlinear Mathematical Modeling and Methods laboratory shanghai Key laboratory for Contemporary Applied mathematics School of Mathematical sciences Fudan University Shanghai China School of Mathematical sciences Fudan University Shanghai China Department of mathematics North University of China Taiyuan China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： nonlinear wave equation Cauchy problem Lifespan

THE MODULI SPACE OF COMPLEX LAGRANGIAN SUBMANIFOLDS IN THE HYPER-KAEHLER MANIFOLD

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Chinese Annals of mathematics,Series B 1999年第4期20卷 393-400页

作者： FU JIXIANG(Institute of mathematics, fudan university, shanghai 200433, china) Institute of mathematics Fudan University Shanghai 200433 China

The deformation of a compact complex Lagrangian submanifold in a hyper-Kaehler manifold and the moduli space are studied. It is proved that the moduli space Mc1 is a special Kaehler manifold, where special means that there is a real flat torsionfree symplectic connection satisfying dI = 0 (I is a complex structure of Mcl). Thus, following [4], one knows thatT*Mcl is a hyper-Kaehler manifold and then that Mcl is a complex Lagrangian submanifold in T* Mcl.

关键词： Moduli space Complex Lagrangian submanifold Hyper-Kaehler manifold Special Lagrangian submanifold Special Kaehler manifold Deformation

THE OCCUPATION DENSITY FIELD FOR THE CATALYTIC SUPER-BROWNIAN MOTION

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Chinese Annals of mathematics,Series B 1999年第4期20卷 447-454页

作者： HONG WENMING(Institute of mathematics, fudan university shanghai 200433, china) Institute of mathematics Fudan University Shanghai 200433 China

It is proved that the occupation time of the catalytic super-Brownian motion is absolutely continuous for d = 1, and the occupation density field is jointly continuous and jointly Holder continuous.

关键词： Branching rate functional Brownian collision local time Catalytic super-Brownian motion Occupation time Occupation density field

TOTAL GENERALIZED MINIMUM BACKWARD ERROR ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS

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Journal of Computational mathematics 1998年第6期16卷 539-550页

作者： Zhi-hao Cao (Dearptment of mathematics, fudan university, shanghai 200433, china) 复旦大学数学系上海

This paper extendes the results by E.M. Kasenally([7]) on a Generalized Minimum Backward Error Algorithm for nonsymmetric linear systems Ax = b to the problem in which pertubations are simultaneously permitted on A and b. The approach adopted by Kasenally has been to view the approximate solution as the exact solution to a perturbed linear system in which changes are permitted to the matrix A only. The new method introduced in this paper is a Krylov subspace iterative method which minimizes the norm of the perturbations to both the observation vector b and the data matrix A and has better performance than the Kasenally's method and the restarted GMRES method([12]). The minimization problem amounts to computing the smallest singular value and the corresponding right singular vector of a low-order upper-Hessenberg matrix. Theoratical properties of the algorithm are discussed and practical implementation issues are considered. The numerical examples are also given.

关键词： nonsymmetric linear systems iterative methods backward error